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Probability Theory
course content

Course Content

Probability Theory

Probability Theory

1. Learn Basic Rules
Random VariableBernoulli Trial 1/2Bernoulli Trial 2/2Binomial Probability 1/2Binomial probability 2/2
2. Probabilities of Several Events
Add ProbabilitiesCalculate Connected ProbabilitiesChallengeMultiply probabilitiesDependent probabilitiesLaw of Total ProbabilityBayes Theorem Challenge
3. Conducting Fascinating Experiments
The First ExperimentThe Second ExperimentThe Third ExperimentCombine Your Knowledge
4. Discrete Distributions
Discrete Uniform DistributionCalculate Fascinating ProbabilityBernoulli DistributionBinomial DistributionChallengePoisson DistributionChallenge
5. Normal Distribution
Normal DistributionChallenge 1Сhallenge 2

bookCalculate Fascinating Probability

Have you ever wonder that your friends birthday could be any day of the year with equal probability. The probability for each day creates uniform distribution.

Let's recall some functions, but for the uniform distribution (they are a little bit different): For calculating the probability of receiving exactly defined output x :

uniform.pdf(x, loc, scale).

For calculating the probability of receiving output that is bigger than x:

uniform.sf(x, loc, scale)(inclusive).

For calculating the probability of receiving output that is less than x:

uniform.cdf(x, loc, scale)(inclusive).

  • loc is the lower bound of the distribution (minimum value).
  • scale is the upper bound of the distribution (maximum value).

Task

Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:

  1. Import uniform object.
  2. Calculate the probability that he was born after the 152nd day of the year (the 1st of June). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  3. Calculate the probability that he was born before the 243rd day of the year (the 31st of August). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  4. Calculate the probability that he was born before the 243rd day of the year and after the 152nd day of the year.

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Section 4. Chapter 2
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bookCalculate Fascinating Probability

Have you ever wonder that your friends birthday could be any day of the year with equal probability. The probability for each day creates uniform distribution.

Let's recall some functions, but for the uniform distribution (they are a little bit different): For calculating the probability of receiving exactly defined output x :

uniform.pdf(x, loc, scale).

For calculating the probability of receiving output that is bigger than x:

uniform.sf(x, loc, scale)(inclusive).

For calculating the probability of receiving output that is less than x:

uniform.cdf(x, loc, scale)(inclusive).

  • loc is the lower bound of the distribution (minimum value).
  • scale is the upper bound of the distribution (maximum value).

Task

Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:

  1. Import uniform object.
  2. Calculate the probability that he was born after the 152nd day of the year (the 1st of June). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  3. Calculate the probability that he was born before the 243rd day of the year (the 31st of August). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  4. Calculate the probability that he was born before the 243rd day of the year and after the 152nd day of the year.

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

Section 4. Chapter 2
toggle bottom row

bookCalculate Fascinating Probability

Have you ever wonder that your friends birthday could be any day of the year with equal probability. The probability for each day creates uniform distribution.

Let's recall some functions, but for the uniform distribution (they are a little bit different): For calculating the probability of receiving exactly defined output x :

uniform.pdf(x, loc, scale).

For calculating the probability of receiving output that is bigger than x:

uniform.sf(x, loc, scale)(inclusive).

For calculating the probability of receiving output that is less than x:

uniform.cdf(x, loc, scale)(inclusive).

  • loc is the lower bound of the distribution (minimum value).
  • scale is the upper bound of the distribution (maximum value).

Task

Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:

  1. Import uniform object.
  2. Calculate the probability that he was born after the 152nd day of the year (the 1st of June). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  3. Calculate the probability that he was born before the 243rd day of the year (the 31st of August). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  4. Calculate the probability that he was born before the 243rd day of the year and after the 152nd day of the year.

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

Have you ever wonder that your friends birthday could be any day of the year with equal probability. The probability for each day creates uniform distribution.

Let's recall some functions, but for the uniform distribution (they are a little bit different): For calculating the probability of receiving exactly defined output x :

uniform.pdf(x, loc, scale).

For calculating the probability of receiving output that is bigger than x:

uniform.sf(x, loc, scale)(inclusive).

For calculating the probability of receiving output that is less than x:

uniform.cdf(x, loc, scale)(inclusive).

  • loc is the lower bound of the distribution (minimum value).
  • scale is the upper bound of the distribution (maximum value).

Task

Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:

  1. Import uniform object.
  2. Calculate the probability that he was born after the 152nd day of the year (the 1st of June). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  3. Calculate the probability that he was born before the 243rd day of the year (the 31st of August). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  4. Calculate the probability that he was born before the 243rd day of the year and after the 152nd day of the year.

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Section 4. Chapter 2
Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
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